This question poses some serious problems for those who believe in Scripture alone as ones authority in right-Christian living. Since Scripture nowhere indentifies the Book of James as divinely inspired for example means that one must go to an authority other than Scripture to determine if it is indeed inspired Scripture. The same applies to any book that one might consider divinely inspired (literally translated as ‘God-breathed’).
If one looks at historical texts of the first century after Jesus’ death and resurrection, even those that are against the Christian church, we find unanimous agreement that the followers of Jesus believed that Jesus actually rose, body and soul, into heaven. They believed it so deeply that they were willing to die instead of denying it. Certainly if Christ had not risen his first disciples (the original 12 chosen by Christ Himself) would not have died horrible deaths affirming the reality and truth of the resurrection. The result of this line of reasoning is that we must conclude that Jesus indeed rose from the dead. Consequently, his claims concerning himself—including his claim to be God—have credibility. He meant what he said and did what he said he would do.
Further, Christ said he would found a Church. Both the Bible (still taken as merely a historical book, not yet as an inspired one) and other ancient works attest to the fact that Christ established a Church with the rudiments of what we see in the Catholic Church today—papacy, hierarchy, priesthood, sacraments, and teaching authority.
We have thus taken the material and purely historical and concluded that Jesus founded the Catholic Church. Because of his Resurrection we have reason to take seriously his claims concerning the Church, including its authority to teach in his name.
This Catholic Church tells us the Bible is inspired, and we can take the Church’s word for it precisely because the Church is infallible. Only after having been told by a properly constituted authority—that is, one established by God to assure us of the truth concerning matters of faith—that the Bible is inspired can we reasonably begin to use it as an inspired book.
For a more detailed look at the inspiration of Sacred Scripture please go to: